# Publications

### Recent Publications

1. ArXiv New infinite hierarchies of polynomial identities related to the Capparelli partition theorems, with Alexander Berkovich. (due to be announced on Monday June 21, 2021)
2. ArXiv Reflecting (on) the modulo 9 Kanade-Russell (conjectural) identities, with Wadim Zudilin. (submitted)
3. ArXiv Cylindric Partitions and some new $A_2$ Rogers-Ramanujan Identities, with Sylvie Corteel and Jehanne Dousse. (accepted, Proc. Amer. Math. Soc.)
4. ArXiv qFunctions – A Mathematica package for q-series and partition theory applications, with Jakob Ablinger. Journal of Symbolic Computation 107 (2021), 145-166.
5. ArXiv Logconcavity results for a biparametric and an elliptic extension of the q-binomial coefficients, with Michael Schlosser and  Koushik Senapati. Int. J. Number Theory 17 (2021), no. 3, 787–804.
6. ArXiv Where do the maximum absolute q-series coefficients of $(1-q)(1-q^2)(1-q^3)\dots(1-q^{n-1})(1-q^n)$ occur?, with Alexander Berkovich.
7. ArXiv On a weighted spin of the Lebesgue Identity. Mathematical Aspects of Computer and Information Sciences. MACIS 2019. Lecture Notes in Computer Science, vol 11989. Springer, Cham. https://doi.org/10.1007/978-3-030-43120-4_20
8. ArXiv A Polynomial Identity Implying Schur’s Partition Theorem. Proc. Amer. Math. Soc. 148 (2020), 3307-3324
9. ArXiv On Double Sum Generating Functions in Connection with Some Classical Partition Theorems. (submitted)
10. ArXiv Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series Identities, with Alexander Berkovich. Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra. Texts & Monographs in Symbolic Computation (A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria). Springer, Cham. https://doi.org/10.1007/978-3-030-44559-1_4
11. ArXiv Elementary Polynomial Identities Involving q-Trinomial Coefficients, with Alexander Berkovich. Ann. Comb. 23 (2019), 549–560.
12. ArXiv Polynomial Identities Implying Capparelli’s Partition Theorems, with Alexander Berkovich. J. Number Theory 201 (2019), 77-107.
13. ArXiv Some Elementary Partition Inequalities and Their Implications, with Alexander Berkovich. Ann. Comb. 23 (2019), 263-284.
14. ArXiv Weighted Rogers-Ramanujan Partitions and Dyson Crank.  Ramanujan J. 46 (2018), no. 2, 579–591.
15. ArXiv On Some Polynomials and Series of Bloch-Polya Type, with Alexander Berkovich. Proc. Amer. Math. Soc. 146 (2018), no. 7, 2827–2838.
16. ArXiv New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions, with Alexander Berkovich. ALLADI 60 2016: Analytic Number Theory, Modular Forms and q-Hypergeometric Series (2017) pp 69-94 Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 221)
17. ArXiv Variation on a theme of Nathan Fine. New weighted partition identities, with Alexander Berkovich. J. Number Theory 176 (2017), 226–248.
18. ArXiv On partitions with fixed number of even-indexed and odd-indexed odd parts, with Alexander Berkovich. J. Number Theory 167 (2016), 7–30.
19. ArXiv A New Companion to Capparelli’s Identities, with Alexander Berkovich. Adv. in Appl. Math. 71 (2015), 125–137.

### Extended Abstracts

1. The DEWCAD Project: Pushing Back the Doubly Exponential Wall of Cylindrical Algebraic Decomposition, with Russell Bradford, James H. Davenport, Matthew England, and Amirhossein Sadeghimanesh. ISSAC 2021 Short Communications
2. On q-Rising Factorials and the Necessity of Shared Memory Calculations. Austrian High-Performance-Computing meeting (AHPC2020), Publisher: Institute of Science and Technology Austria, Klosterneuburg Austria, Editors: Alois Schlögl et al. ISBN: 978-3-99078-004-6

### Soon to be Public

• On two new conjectural sum-product identities modulo 6, joint with George E. Andrews
• Counting  on 4-decorated diagrams.

### Referee Work

Advances in Applied Mathematics, American Mathematical Monthly, Annales Henri Poincaré D (Physics and combinatorics), Annals of Combinatorics, Discrete Mathematics, Integral Transforms and Special Functions, International Journal of Number Theory, Journal of Combinatorial Theory – Series A, Journal of Integer Sequences, Journal of Difference Equations and Applications, Journal of Number Theory,  Journal of Symbolic Computation, Proceedings of the American Mathematical Society, Ramanujan Journal, Research in Number Theory, Turkish Journal of Mathematics.